McKean-Vlasov stochastic differential equations (MV-SDEs) provide a
mathematical description of the behavior of an infinite number of interacting
particles by imposing a dependence on the particle density. As such, we study
the influence of explicitly including distributional information in the
parameterization of the SDE. We propose a series of semi-parametric methods for
representing MV-SDEs, and corresponding estimators for inferring parameters
from data based on the properties of the MV-SDE. We analyze the characteristics
of the different architectures and estimators, and consider their applicability
in relevant machine learning problems. We empirically compare the performance
of the different architectures and estimators on real and synthetic datasets
for time series and probabilistic modeling. The results suggest that explicitly
including distributional dependence in the parameterization of the SDE is
effective in modeling temporal data with interaction under an exchangeability
assumption while maintaining strong performance for standard It\^o-SDEs due to
the richer class of probability flows associated with MV-SDEs.

将分布依赖显式地包含在随机微分方程的参数化中对于建模具有交互性的时间数据是有效的，并在维持标准 Itô-SDE 的优越性能的同时，通过 MV-SDE 关联的更丰富的概率流类来进行时间数据的建模。

神经麦克林 - 瓦萨夫过程：扩散过程中的分布依赖

Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion  Processes

Diffusion models have emerged as a powerful new family of deep generative
models with record-breaking performance in many applications, including image
synthesis, video generation, and molecule design. In this survey, we provide an
overview of the rapidly expanding body of work on diffusion models,
categorizing the research into three key areas: efficient sampling, improved
likelihood estimation, and handling data with special structures. We also
discuss the potential for combining diffusion models with other generative
models for enhanced results. We further review the wide-ranging applications of
diffusion models in fields spanning from computer vision, natural language
generation, temporal data modeling, to interdisciplinary applications in other
scientific disciplines. This survey aims to provide a contextualized, in-depth
look at the state of diffusion models, identifying the key areas of focus and
pointing to potential areas for further exploration. Github:
this https URL.

本文概述了 “扩散模型” 在图像合成、视频生成、分子设计等领域中的应用，并将相关研究分为三大类：高效采样、改进似然估计和处理具有特殊结构的数据。此外，还探讨了将扩散模型与其他生成模型相结合以获得更好结果的潜能，在计算机视觉、自然语言生成、时态数据模型等领域具有广泛的应用。本文旨在提供一个全面的扩散模型综述，指出其重点研究领域并指向未来的研究方向。